Formation and Observation of a Quasi-Two-Dimensional $d_{xy}$ Electron Liquid in Epitaxially Stabilized ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{TiO}}_4$ Thin Films

We report the formation and observation of an electron liquid in ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{TiO}}_4$, the quasi-two-dimensional counterpart of ${\mathrm{SrTiO}}_3$, through reactive molecular-beam epitaxy and in situ angle-resolved photoemission spectroscopy. The lowest lying states are found to be comprised of Ti $3d_{xy}$ orbitals, analogous to the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface and exhibit unusually broad features characterized by quantized energy levels and a reduced Luttinger volume. Using model calculations, we explain these characteristics through an interplay of disorder and electron-phonon coupling acting cooperatively at similar energy scales, which provides a possible mechanism for explaining the low free carrier concentrations observed at various oxide heterostructures such as the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface.

Figure 1

(a) Diagram of the crystal structure of ${\mathrm{Sr}}_2{\mathrm{TiO}}_4$. (b) DFT band calculations of ${\mathrm{Sr}}_2{\mathrm{TiO}}_4$, showing the lowest unoccupied band of $d_{xy}$ character. The left enlarged plot shows a rigid band shift of 5% electron doping. (c) An epitaxial La-doped ${\mathrm{Sr}}_2{\mathrm{TiO}}_4$ thin film shows orders of magnitude lower resistivity than a bulk polycrystalline sample [16]. (d) X-ray diffraction and rocking curves of the 006 diffraction peak of 5% and 15% La-doped ${\mathrm{Sr}}_2{\mathrm{TiO}}_4$ films. The x-ray diffraction scans are offset for clarity and the substrate peaks are marked with asterisks ($*$).

Figure 2

(a) ARPES isoenergy intensity map with an integration window of $E_F+/-10\mathrm{meV}$ of 5% La-doped ${\mathrm{Sr}}_2{\mathrm{TiO}}_4$ shows a single circular pocket centered at the Brillouin zone center. The red marks indicate the extracted Fermi momenta via fits of momentum distribution curves (MDCs) and the green dashed line is the expected Fermi momenta. (b) Integrated EDC of the valence band indicates a gap of $\sim 4\mathrm{eV}$. (c),(d) XPS measurements reveal 4.0% and 14.4% lanthanum concentrations in nominal 5% and 15% doped films, respectively.

Figure 3

(a),(b) ARPES spectra taken along the (0,0)-($0,\pi$) direction of the 5% and 15% La-doped ${\mathrm{Sr}}_2{\mathrm{TiO}}_4$ films. The blue symbols mark the peak positions from Gaussian fits to the MDCs. The green and red curves are DFT calculated bands and parabolic fits to the peak positions, respectively. (c),(d) The second derivative plots and (e),(f) the EDCs show quantized states with a periodic separation of 93 meV for both films. The EDCs are integrated $\pm 0.01\AA$ around Fermi momenta and the shifts from $E_F$ could be due to the experimental resolution. (g),(h) The Gaussian fits to the MDCs reveal FWHMs of $0.14{\AA }^{-1}$ and $0.18{\AA }^{-1}$ of the 5% and 15% doped samples, respectively.

Figure 4

Calculated ARPES spectra considering (a) $e\text{−}\mathrm{ph}$ coupling for $\lambda =0.15$ only ($\lambda$ is defined by Eq. (4) in the Supplemental Material [11]), (b) disorder only, and (c) both $e\text{−}\mathrm{ph}$ coupling and disorder, showing the important interplay of $e\text{−}\mathrm{ph}$ coupling and disorder. (d) The second derivative of (c), demonstrating the quantization of quasilocalized electronic states.